arb_hypgeom_central_bin_ui
Synopsis
#include <flint/arb_hypgeom.h>For n \le 17 the value comes from a table and for n < 6\,\mathit{prec} + 200 from the exact integer fmpz_bin_uiui. For larger n the function sums the asymptotic expansion of \binom{2n}{n} \sqrt{\pi n} / 4^n in powers of 1/n^2, whose coefficients involve Bernoulli numbers, with the rigorous error bound of Brent [Bre2016].
References#
- [Bre2016] R. P. Brent. Asymptotic approximation of central binomial coefficients with rigorous error bounds. Preprint, 2016. https://arxiv.org/abs/1608.04834
Cite this page
The FLINT team, “arb_hypgeom_central_bin_ui (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_central_bin_ui.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-central-bin-ui,
author = {{The FLINT team}},
title = {{arb\_hypgeom\_central\_bin\_ui (arb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_central_bin_ui.html},
note = {Generated 2026-10-20}
}